author = "Gutman A.E.",

title = "Locally one-dimensional K-spaces and $\sigma$-distributive Boolean algebras",

journal = "Siberian Adv. Math.",

year = "1995",

volume = "5",

number = "1",

pages = "42--48",

annote = "It is known that all band preserving operators acting in a universally complete K-space are regular if and only if the K-space is locally one-dimensional. In addition, a K-space with base $B$ is locally one-dimensional if and only if $R^{\land}=R$ in $V^{(B)}$. It seems to have been unknown so far whether there exist nondiscrete locally one-dimensional K-spaces. In the present note we give a positive answer to the question. As an auxiliary result, we establish that a K-space is locally one-dimensional if and only if its base is $\sigma$-distributive.",

keywords = "locally one-dimensional K-space, discrete K-space, $\sigma$-distributive Boolean algebra, $\sigma$-inductive Boolean algebra, atomic Boolean algebra, regular operator, real numbers in a Boolean-valued universe"